Hoeffding's inequalities: A counterexample |
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Authors: | Torben Maack Bisgaard |
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Affiliation: | (1) Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 København Ø, Denmark |
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Abstract: | A sequence : 0 satisfiesHoeffding's inequality of order n if wheneverX1,...,Xn are independent nonnegative integer-valued elementary random variables and are independent identically distributed nonnegative integer-valued elementary random variables, the common distribution of which is the average of those ofX1,...,Xn. We show that for each integerm greater than 2 there exists a sequence satisfying Hoeffding's inequality of every order greater thanm but not that of orderm. This answers a question raised by Berg, Christensen, and Ressel. |
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Keywords: | Hoeffding's inequalities negative definite sequence completely negative definite sequence |
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